GARCH Model Change Point Detection And Its Application In Oil Price Fluctuation Analysis

As the "unicorn" of time series problems,the study of change-point detection has received widespread attention and development from scholars at home and abroad in recent decades.In nature,the long-term development of things is often accompanied by qualitative or quantitative changes,which is the basis for the reality of change-point detection.At the theoretical level,this is often manifested as a sudden change in the data from a certain moment or location,which no longer follows the previous regular distribution,i.e.a change point has appeared.Consideration of the number and location of variation points has also become a major part of research into the problem of variation point detection in time series data.Since the 1960 s,research methods such as the least squares method,the maximum likelihood method,the Bayes method,the cumulative sum of squares method,the local comparison method and the wavelet analysis method have been developed,and the framework for estimating and detecting variation points has been continuously improved.In this thesis,we analyse the problem of variation point detection in GARCH models based on Bayesian statistical inference.Compared with foreign research,there is room for enriching the theoretical and applied aspects of the variation point detection methods based on Bayesian statistical inference in China.In daily life,daily or monthly time series data are susceptible to change due to real world factors,and such changes are classified as abrupt or gradual depending on their intensity.As it is appropriate to fit a heteroskedasticity time series model to the crude oil price series,this thesis determines the number and location of variation points and the changes in the parameters of the GARCH model before and after the variation points,using a Bayesian approach to detect sudden changes in the crude oil price series.At the theoretical level,this thesis will focus on the GARCH(1,1)model for variation detection analysis,discussing the detection theory for the single-variation point case and the multi-variation point case respectively,and deriving the conditional posterior distribution for the error terms obeying the normal distribution and the standard t-distribution respectively.At the application level,a total of 5,806 daily WTI crude oil price data from January 4,2000 to February 14,2023 are firstly selected,and then the Bayesian statistical inference idea,MCMC method and Gibbs sampling technique are used to identify the variation points in the cases with posterior probability P greater than 0.8 and 0.9 and the parameter estimation of the GARCH model for a given sample interval to determine The time at which the mutation point occurred and further analysis of the possible causes of the mutation were carried out.Finally,any one of the mutation points was selected and the GARCH model was fitted and the parameters estimated for the series before and after the mutation point.The study shows that the Bayes-based variation detection method can detect the parameter changes of the GARCH model before and after the variation point more accurately,and that the generation of abrupt variation points in crude oil price series is indeed traceable in real life.In general,this thesis further analyses the change point detection problem of Bayesian-based GARCH(1,1)models,identifies the historical change points of daily WTI crude oil price data and the time of occurrence of the change points,and finally analyzes the possible causes of sudden price changes,which is of certain practical significance.